Mathematical modeling of the propagation of precursors of the front edges of cracks as spatial curves on the fronts of waves of a strong discontinuity of rates and stresses

Abstract

Crack propagation occurs at the macro level with finite elastic displacements, deformations and stresses far from the front edge of the crack. In the neighborhood of the front spatial edge of a crack during its development, the behavior of the material is really inelastic, when the changes take place at the micro and nano levels.In this paper with the use of the Bingham model of an elasto viscoplastic (EVP) material, a small δ-neighborhood is chosen around the front spatial edge of a crack. The neighborhood has the shape of a cylinder with a curvilinear axis. It is shown that the wave fronts of plastic deformation are waves of longitudinal or transverse deformation and bear the front edges of the precursors these are longitudinal shear cracks and transverse shear cracks or detachment cracks.Ordinary differential equations of transfer of the intensity of tangential shear stresses and normal detachment stresses behind the precursor of the crack edge depending on the path traveled by the front edge of the crack are constructed. Exact solutions are obtained in the case of a non-stressed material. The finiteness of the length of a growing crack in an EVP material has made it possible to clarify the classical criteria for brittle fracture.